Extracting, Tracking and Visualizing Vortices in 3D Complex-Valued Superconductor Simulation Data

We propose a unified method for the analytically exact vortex extraction and tracking of superconducting magnetic flux vortices for both structured and unstructured mesh data. In the Ginzburg-Landau theory, magnetic flux vortices are well-defined features in a complex-valued order parameter field, and their dynamics determine electromagnetic properties in type-II superconductors. Our method represents each vortex line (a 1D curve embedded in 3D space) as a connected graph extracted from the discretized field in both space and time. This method, which uses no approximations, represents the most exact tracking that can be performed on a set of curves in a time-varying discretized complex scalar field. We then apply 3D visualization and 2D event diagrams to the extraction and tracking results to help scientists understand vortex dynamics and macroscale superconductor behavior in greater detail than previously possible.